What is the term for the stone tool technology most often associated with the neandertals that extended across europe and north africa, into the former soviet union, israel, iran, central asia and possibly china?

The correct answer is Mousterian. These tools made out of stone, that is, flint tools, were common among neanderthals and have been historically found almost anywhere in the world where there was a civilization. The flint wasn't only used for tools however, but weaponry also, with things like flint arrow tips being found as well and also spears.